Respuesta :
Answer
a) y-intercept = 20 dollars
In the context of the question, this means that the cost per month of the data usage on that smartphone is 20 dollars.
b) Slope = 0.03 dollars per megabyte
In the context of the question, this means that the cost of data per megabyte is $0.03
c) y = 0.03x + 20
Check Explanation for the second question.
Explanation
a) The y-intercept is the point where the line crosses the y-axis, that is, the value of y when x = 0
From the attached graph, we can see that the graph crosses the y-axis at
y = 20 dollars
In the context of the question, this means that the cost per month of the data usage on that smartphone is 20 dollars.
b) For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question, we will pick two points
(x₁, y₁) and (x₂, y₂) are (0, 20) and (2000, 80)
[tex]\text{Slope = }\frac{80-20}{2000-0}=\frac{60}{2000}=\text{ 0.03}[/tex]Slope = 0.03 dollars per megabyte
In the context of the question, this means that the cost of data per megabyte is $0.03
c) Since this is a straight line,
The slope and y-intercept form of the equation of a straight line is given as
y = mx + c
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
c = y-intercept of the line.
For this question,
y = Cost of data per month
m = slope = 0.03 dollars per megabyte
x = data usage in megabytes
c = y-intercept = 20
y = 0.03x + 20
For the second question,
We are asked to find the slope and y-intercept of each line
We've explained how to get the slope and y-intercept the other time
a) (x₁, y₁) and (x₂, y₂) are (0, -1) and (2, 3)
[tex]\text{Slope = }\frac{3-(-1)}{2-0}=\frac{3+1}{2}=\frac{4}{2}=2[/tex]And we can evidently see that the line crosses the y-axis at the point y = -1. So, y-intercept = c = -1
The slope and y-intercept form of the equation of a straight line is given as
y = mx + c
where
y = y-coordinate of a point on the line.
m = slope of the line = 2
x = x-coordinate of the point on the line whose y-coordinate is y.
c = y-intercept of the line = -1
y = 2x - 1
b) (x₁, y₁) and (x₂, y₂) are (4, -2) and (0, 2)
[tex]\text{Slope = }\frac{2-(-2)}{0-4}=\frac{2+2}{-4}=\frac{4}{-4}=-1[/tex]And we can evidently see that the line crosses the y-axis at the point y = 2. So, y-intercept = c = 2
The slope and y-intercept form of the equation of a straight line is given as
y = mx + c
where
y = y-coordinate of a point on the line.
m = slope of the line = -1
x = x-coordinate of the point on the line whose y-coordinate is y.
c = y-intercept of the line = 2
y = -x + 2
c) (x₁, y₁) and (x₂, y₂) are (-3, 3) and (3, -1)
[tex]\text{Slope = }\frac{-1-3}{3-(-3)}=\frac{-4}{3+3}=\frac{-4}{6}=-\frac{2}{3}[/tex]To find the y-intercept for this, we will use one of the given points and (0, c) to find c
(x₁, y₁) and (x₂, y₂) are (-3, 3) and (0, c)
Slope = -(2/3)
[tex]\begin{gathered} \text{Slope = }\frac{c-3}{0-(-3)} \\ -\frac{2}{3}=\frac{c-3}{0+3} \\ -\frac{2}{3}=\frac{c-3}{3} \\ \text{Cross multiply} \\ 3(c-3)=3(-2) \\ 3c-9=-6 \\ 3c=-6+9 \\ 3c=3 \\ \text{Divide both sides by 3} \\ \frac{3c}{3}=\frac{3}{3} \\ c=1 \end{gathered}[/tex]The slope and y-intercept form of the equation of a straight line is given as
y = mx + c
where
y = y-coordinate of a point on the line.
m = slope of the line = -(2/3)
x = x-coordinate of the point on the line whose y-coordinate is y.
c = y-intercept of the line = 1
y = (-2/3)x + 1
d) (x₁, y₁) and (x₂, y₂) are (4, 0) and (2, -1)
[tex]\text{Slope = }\frac{-1-0}{2-4}=\frac{-1}{-2}=\frac{1}{2}[/tex]To find the y-intercept for this, we will use one of the given points and (0, c) to find c
(x₁, y₁) and (x₂, y₂) are (4, 0) and (0, c)
Slope = (1/2)
[tex]\begin{gathered} \text{Slope = }\frac{c-0}{0-4} \\ \frac{1}{2}=\frac{c}{-4} \\ \text{Cross multiply} \\ 2c=-4 \\ \text{Divide both sides by 2} \\ \frac{2c}{2}=-\frac{4}{2} \\ c=-2 \end{gathered}[/tex]The slope and y-intercept form of the equation of a straight line is given as
y = mx + c
where
y = y-coordinate of a point on the line.
m = slope of the line = (1/2)
x = x-coordinate of the point on the line whose y-coordinate is y.
c = y-intercept of the line = -2
y = (½)x - 2
Hope this Helps!!!
